
There are reasons to expect the Poisson module to be misspecified [1]}.
The relaxation of the Poisson likelihood under \(\delta \) -SMI is defined by
\(p_\delta ( Y_i \mid \varphi , \tilde{\theta }) = \sum _{{\tilde{Y}}_i=0}^\infty p( {\tilde{Y}}_i \mid \varphi , \tilde{\theta })K_{\delta }(Y_i,{\tilde{Y}}_i).\) 
